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<p><dfn class="terminology">Solution:</dfn> The equation can be arranged as</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation*}
y^{\prime \prime}+\frac{3 x}{x (x-4)} y^{\prime}+\frac{4}{x (x-4)} y=\frac{2}{x(x-4)}.
\end{equation*}
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<p class="continuation"><span class="process-math">\(p(x)\text{,}\)</span> <span class="process-math">\(q(x)\)</span> and <span class="process-math">\(g(x)\)</span> are continuous for <span class="process-math">\(x \neq 0\)</span> and <span class="process-math">\(x \neq 4\text{,}\)</span> i.e., in <span class="process-math">\(-\infty&lt;x&lt;0\)</span> or <span class="process-math">\(0&lt;x&lt;4\)</span> or <span class="process-math">\(4&lt;x&lt;\infty\text{.}\)</span> The interval <span class="process-math">\(0&lt;x&lt;4\)</span> contains <span class="process-math">\(x=3\text{.}\)</span> Thus, it is the largest interval in which there is a unique solution.</p>
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